(This is not the adjoint of operator in (REF ), but rather
defined by analogy with the case \(X\)  trivial.) It is shown in
[1]} that if \((A,u)\)  is stable then the set
\( W_{A,u} = \lbrace  (A + a, \exp _u(\xi )), (a,\xi ) \in  \operatorname{ker}{\operatorname{d}}_{A,u}^*\rbrace  \) 
